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arXiv · 2603.03093

Orthogonal polynomials in de Branges--Rovnyak spaces

Eugenio Dellepiane·Daniel Seco
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Abstract

Given a function $b$, holomorphic on the disc and bounded by 1, one can construct an associated reproducing kernel Hilbert space called the de Branges--Rovnyak space $H(b)$. We explore representations of such spaces via descriptions of the corresponding families of orthogonal polynomials. We find relevant structures in the linear systems involved in a diversity of cases when $b$ is rational. We also establish a form of invariance under some composition operators on $H(b)$ spaces.

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Eugenio Dellepiane, Daniel Seco. 2026-03-03. Orthogonal polynomials in de Branges--Rovnyak spaces. https://arxiv.org/abs/2603.03093

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